Oscillations practice · Mixed difficulty

The bob of a pendulum is in the lowest position and has a horizontal velocity of $\sqrt {gL}$ where $L$ is length of the pendulum and $g$ is acceleration due to gravity is given to it. Then the bob

A bob of mass m suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $1/4$ times that of the bob and the length of the thread is increased by $1\mathrm{/}3\,\,\mathrm{rd}$ of the original length, then the time period of the simple harmonic oscillations will be

A particle is executing simple harmonic motion with frequency $f$ . The frequency at which its kinetic energy change into potential energy is

If a simple harmonic is represented by $\frac{{{d^2}x}}{{d{t^2}}}$$+ \alpha x = 0$,its time period is

Two pendulums of length 121 cm and 100 cm start vibrating. At same instant the two are in the mean position in the same phase. After how many vibrations of the shorter pendulum, the two will be in phase in the mean position?

If a body oscillates at the angular frequency ${\omega _d}$ of the driving force, then the oscillations are called

Which one of the following is simple harmonic?

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion

The time period of a simple pendulum measured inside a stationary elevator is $4 {~s}$. If the lift start accelerating downwards with an acceleration $3 g / 4$, the time period will be

Which of the following quantities is always negative in SHM?
Here, $\mathbf{s}$ is displacement from mean position.

Assertion: A heavy metal sphere is suspended by a spring. When pulled down a little and released, it oscillates up and down with a frequency $f.$ If it is taken to the moon where the acceleration due to gravity is $g/6,$ the frequency of oscillation is $\sqrt{6}f$.
Reason: The frequency of oscillation of the spring depends only on the mass of the sphere and spring constant.

The time period of a simple pendulum is $T$. If its point of suspension is moved upward according to relation $y=\lambda t^2$ where $\lambda$ is a constant then its new time period $T_1$.

A simple pendulum is made of bob which is a hollow sphere full of sand suspended by means of a wire. If all the sand is drained out, the period of the pendulum will

A mass of 2 kg attached to a spring of force constant $260^\circ \,\,\,N{m^{ - 1}}$ makes 200 oscillations. What is the time taken [in seconds] nearly?

A plate oscillates with time period $'T'$. Suddenly, another plate put on the first time, then time period

Two particles $P$ and $Q$ describe SHM of same amplitude $a$ and frequency $v$ along the same straight line. The maximum distance between two particle is $\sqrt{2} a$. The initial phase difference between the particles is

For a SHO, if the magnitudes of maximum velocity and acceleration are equal, its frequency of oscillations is

The elongation of spring of length $L$ and of negligible mass due to a force is $x$. the spring is cut into two pieces of length in ratio $1: n$. The ratio of the respective spring constants is:

A particle executes SHM with a time period of $2 \mathrm{~s}$ and amplitude $5 \mathrm{~cm}.$ Find displacement after $1 / 3$ second; starting from the mean position.

$F-x$ equation of a body in SHM along ${x}$-axis is $F+12 x=0$. Here, $F$ is in newton and $x$ in metre. If the mass of the body is $3 {~kg}$, then the time period of oscillations is;

The force constant of two springs are$\;{K_1}$ and ${K_2}$ Both are stretched till their elastic energies are equal. If the stretching forces are ${F_1}$ and ${F_2},$ then ${F_1}:{F_2}$ is

A small ball is dropped from a certain height on the surface of a non-viscous liquid of density less than the density of ball. The motion of the ball is

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement

What is the phase difference between velocity and acceleration of a particle executing SHM?

A horizontally placed spring mass system has time period $T$. The same system is now placed on a car moving with acceleration $a$ in horizontal direction. Then,

A body is executing simple harmonic motion with frequency '$n$' the frequency of its potential energy is

A particle performs Simple Harmonic Motion of amplitude ${A}$ and angular frequency $\omega$ along a straight line. When it is at a distance $\frac{\sqrt{3}}{2} {~A}$ from mean position, its kinetic energy gets increased suddenly by an amount $\frac{1}{2} m \omega^2 A^2$, due to an impulsive force. Then new amplitude of oscillations of the particle will be :

A second's pendulum is taken in a carriage. Find the period of oscillation when the carriage moves with an acceleration of $4 \mathrm{~ms}^{-2}$ (i) vertically upwards (ii) vertically downwards, and (iii) in a horizontal direction.

The differential equation of a particle executing simple harmonic motion along $y$-axis is

Spring force is a